Simple Interest
Math MCQs

Question :    How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

Correct Answer  $7050

Solution & Explanation

Solution

Given,

Amount (A) = $8812.5

Rate of Simple Interest (R) = 5%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$8812.5 = P (1 + 5% × 5)

⇒ $8812.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8812.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8812.5 = P (1 + ²⁵/₁₀₀)

⇒ $8812.5 = P (^{100 + 25}/₁₀₀)

⇒ $8812.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8812.5

⇒ P = ^8812.5/_¹²⁵/100

⇒ P = 8812.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8812.5 × 100}/₁₂₅

⇒ P = ⁸⁸¹²⁵⁰/₁₂₅

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8812.5, then the Principal = ¹⁰⁰/₁₂₅ × 8812.5

= ^{100 × 8812.5}/₁₂₅

= ⁸⁸¹²⁵⁰/₁₂₅

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(2) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.

(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?

(4) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.

(7) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?

(9) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.